A365724 - OEIS

%I #11 Sep 17 2023 10:11:03

%S 1,0,0,1,1,0,3,7,4,12,45,55,77,286,546,728,1960,4760,7548,15504,39729,

%T 75582,140448,336490,723327,1366200,2992990,6758895,13522275,28094040,

%U 63183315,133231800,273896532,600805296,1305229332,2720740792,5843241088,12797739672

%N G.f. satisfies A(x) = 1 + x^3*A(x)^3*(1 + x*A(x)).

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(k,n-3*k) * binomial(n+1,k).

%o (PARI) a(n) = sum(k=0, n\3, binomial(k, n-3*k)*binomial(n+1, k))/(n+1);

%Y Cf. A308616, A365723, A365725, A365726.

%Y Cf. A001005, A001006, A365730.

%Y Cf. A114997.

%K nonn

%O 0,7

%A _Seiichi Manyama_, Sep 17 2023